Synergy of dual-atom catalysts deviated from the scaling relationship for oxygen evolution reaction

Dual-atom catalysts, particularly those with heteronuclear active sites, have the potential to outperform the well-established single-atom catalysts for oxygen evolution reaction, but the underlying mechanistic understanding is still lacking. Herein, a large-scale density functional theory is employed to explore the feasibility of *O-*O coupling mechanism, which can circumvent the scaling relationship with improving the catalytic performance of N-doped graphene supported Fe-, Co-, Ni-, and Cu-containing heteronuclear dual-atom catalysts, namely, M’M@NC. Based on the constructed activity maps, a rationally designed descriptor can be obtained to predict homonuclear catalysts. Seven heteronuclear and four homonuclear dual-atom catalysts possess high activities that outperform the minimum theoretical overpotential. The chemical and structural origin in favor of *O-*O coupling mechanism thus leading to enhanced reaction activity have been revealed. This work not only provides additional insights into the fundamental understanding of reaction mechanisms, but also offers a guideline for the accelerated discovery of efficient catalysts.

2) The overpotential calculation does not account for the barrier for O2 desorption, I guess because it is not an electrochemical process. However, if O2* is largely stable, the barrier for its desorption could be higher than the eta. Did the authors considered this? Figure S5 shows many cases where O2* is strongly stable.
3) Figure 6 and the related discussion look obscure to me. They state that: " Fig. 6a shows that the screened highly active DACs prefer second OH adsorption (except for CoCu) over competitive OH deprotonation, suggesting that these DACs are selective for OCM rather than AEM" If I read correctly the figure in several cases, about half, O* formation is more favorable than OH*OH* one. This point is related to point 1.2. Also, they suggest some correlation between M1-M2 distance and the overpotential, figure 6b, but if I read correctly the figure, the data are broadly scattered.
4) The section devoted to Bader charge analysis, charge density plots etc should be moved to the SI. They make more diluted the main findings.

Reviewer #2 (Remarks to the Author):
In this manuscript, a large-scale DFT was employed to explore the feasibility of *O-*O coupling mechanism, which can circumvent the scaling relationship on improving the OER performance of DACs. In addition, the chemical and structural origin in favor of *O-*O coupling mechanism thus leading to enhanced OER activities have been revealed. However, the analyses of Gibbs free energy and overpotential are probably wrong, the conclusions lack innovative. The reviewer suggests that if the author thoroughly revises this manuscript, it may be reconsidered for publication in this journal.
(2) Unlike the referenced of DACs [J. Mater. Chem. A 10, 8309-8323 (2022).], in this work, the first *OH is adsorbed in the middle of the dual-atom, then the adsorption behavior of the second *OH has a stereo-hindrance effect. Therefore, the different adsorption behavior of the second *OH should be discussed, e.g. on the other side of the catalyst, on the adjacent C atom, etc.
(3) The reason for proposing LOM or even OCM is the fact that *O-*O structures are generally more stable than OO* structures. Firstly, many of the selected DACs do not have this property, and secondly, the energy barrier of the step *O-*O→O2 is generally higher, therefore, the author needs to calculate the transition state, or even the kinetic pathways of the OCM. (4) The mechanism, OCM, that the author summarized, applies to both acidic and alkaline electrolytes. However, like the AEM, the potential-determining step is generally different for acidic and alkaline electrolytes, and the author needs to add discussions based on the calculation results. (5) It is necessary to carefully verify the rightness of the data for the OCM of NiPd@NC, because, the data do not theoretically match the given structures and mechanism. If the data are verified to be right, the author needs to analyze the electronic properties such as Bader charge for each step of the OCM of NiPd@NC. I must say that current level of investigation, and generality of the message is not sufficient for Nature Communications. If the author could provide further and broader evidence of the following major points, I will be happy to recommend publication of the work.

Response:
We really appreciate the reviewer's efforts on reviewing our manuscript and providing us with constructive comments and suggestions to further improve the quality of our paper. All the suggestions and comments have been carefully addressed and modifications have been made accordingly.
Comment 1: The take-home message is unclear, and this strongly harm the potential impact of the work. More specifically, it is unclear whether the main message is one or a combination between the following: 1.1 OER does not follows the typical mechanism.
1.2 The authors are providing a recipe for the catalytic optimization, with a volcano top different from that of conventional catalysts.
1.3 New scaling relationships are provided for OER on DACs.
Each of the mentioned points should be better corroborated by additional calculations or acknowledgement of the existing literature.

Response:
Many thanks for the reviewer's comment. The take-home message we are aiming to present in this manuscript is the potential and feasibility of *O-*O coupling mechanism (OCM) in improving the OER activity on the dual-metal sites. In addition to other paths reported in literatures, we proposed that OCM should also be considered as a possible mechanism, especially when dealing with DACs systems (point 1.1). The more favorable configuration of two *OH adsorption on the M2 dimer can tactfully circumvent the scaling relationship between *OOH and *OH, rendering η closer to the ideal 0 V with significantly enhanced OER activities (point 1.3). More importantly, based on the large-scale screening, we further proposed the chemical and structural conditions for the feasible occurrence of OCM, thus providing a recipe for the catalytic optimization (point 1.2). Therefore, these three aspects are in progressive relation, which construct a new framework on improving the OER activities of DACs systems via unconventional OCM pathway. To strengthen the main purpose of our manuscript, the last Discussion part has been modified in the revised manuscript.

Revisions:
Page 19, Line 20: "This work provides a comprehensive understanding of the OCM mechanism, rendering a new recipe for the catalytic optimization of OER, with a volcano top different from that of conventional AEM. It is important that OCM should be considered as a prominent OER pathway catalyzed by DACs in the future study. These theoretical insights would be also beneficial in designing highperformance catalysts for other electrochemical reactions."

Response:
We thank the reviewer for letting us know these excellent works, wherein new mechanisms were reported as the complement of traditional ones. Similar with these literatures, also inspired by the lattice oxygen mechanism (LOM) that involved two active sites on metal oxide, we want to know if the *O-*O coupling mechanism (OCM) could be operative on two metal centers of DACs. Although the adsorption of two *OH has already been reported on SACs, the importance and generality of their formation on DACs along with their contribution to OER activities have not systematically investigated crossing the entire periodic table so far. Furthermore, no such large-scale DFT screening to explore the feasibility of OCM with the construction of an activity map on DACs has been reported.
The literatures that reviewer mentioned help us deepen the mechanistic understanding of OER on SACs, and we further extended this concept to DACs. All these literatures have been acknowledged in the revised manuscript. In brief, the authors should include the mentioned data to support their assumption, i.e. that the fully unconventional mechanism is the likely one in all or most of the cases.

Response:
Thank you for these insightful comments and suggestions. We agree with the reviewer that the reaction will follow a channel based on the most stable intermediates. Indeed, we noticed the critical role of the most stable intermediates performed in the reaction pathway. Comparing ΔG*OH-*OH-ΔG*OH with ΔG*O-ΔG*OH can determine the more readily generated intermediates. As shown in Figure R1a and Tables R1-R5, it can be found that about half of the DACs exhibited *OH-*OH selectivity, including 6 heteronuclear and 4 homonuclear catalysts screened. In addition, further exploration of catalysts with *OH-*OH selectivity showed that *OH-*OH intermediates were more readily generated as *OH-*O rather than *OOH (Figure R1b and Tables R6-R10). This is because the *OH-*O configuration is energetically more stable than *OOH on the metal dimer structure, which is distinct from SACs ( Figure R2). Since 10 of the screened 11 DACs (except CoCu) possessed *OH-*OH and *OH-*O selectivity, crossing of intermediates between AEM and OCM can be excluded to affect the reactivity ( Figure R3).
Regarding the reviewer's concern, we conducted additional calculations. For the DACs with *O selectivity ( Figure R1a, the pink area), the intricate case of crossing intermediates between OCM and AEM induces the reaction to follow a hybrid pathway (*OH*O*OH-*O*O2O2(g)). As an example, for DACs with *O selectivity shown in Figure R4 Tables R1-R4), the potential determining step (PDS) of all DACs except CoAu is *OH-*O*O2, and hybrid mechanism for crossing intermediates are only effective for ΔG(*OH*O) and ΔG(*O*OH-*O), therefore with limited effect on the catalytic activity of DACs with *O selectivity.
Remarkably, the PDS of CoAu didn't occur at *OH-*O  *O2, which enabled the reaction to bypass the PDS of *OH*OH-*OH (ΔG=1.88eV), reducing the PDS to 1.25eV ( Figure R4c). This indicates that the increase in OER reactivity is feasible for CoAu via the crossing between OCM and AEM intermediates. Nevertheless, as the PDS for the majority of DACs with *O selectivity corresponds to *OH-*O*O2, and the hybrid pathway only contributes to ΔG(*OH*O) and ΔG(*O*OH-*O), there is limited impact on the critical scaling relationship between ΔG*OH and ΔG*OH-*O.
As for the grey line in Figure 4b in the manuscript, it is worth mentioning that other paths are also possible for OER on SACs. These imply the formation of other intermediates than those classical ones, like for instance in the ref [10.1016/j.jcat.2022.12.014]. However, for the purpose of this work, that is elaborating the essential role of the unconventional OCM path on DACs mediated OER, considering the most common traditional path on SACs is sufficient. For more convincing, we further added the data that shows ( Figure R5), not only SACs, but also DACs and metal oxides can hardly break the 0.37V bottleneck, as long as the conventional pathway operated by the grey line.
In summary, by comparing the OCM and AEM intermediates to determine the selectivity of the reactions, it was found that 10 of the 11 high-performance DACs screened completely proceeded with the OCM along the OER process. A minimum overpotential of 0.02 V for CoAu can be achieved due to the crossing of the AEM and OCM reaction intermediates along the hybrid mechanism. The remaining DACs along the hybrid mechanism all showed limited effects on reactivity and all reaction paths (OCM, AEM and hybrid mechanism) always follow the most stable channel. Furthermore, given that the mixing mechanism only operates for ΔG(*OH*O) and ΔG(*O*OH-*O), the scaling relationship between the ΔG*OH and ΔG*OH-*O is considered to remain valid, and the grey line attributed to conventional AEM plays the crucial role in understanding the origin of the breakthrough of the 0.37 V bottleneck via OCM.         15), which resulted in a complicated OER reaction network of the SACs."    I would like to point out, that the inclusion of the additional results could boost the impact of the authors' findings, providing a generality to the already interesting message. At the current stage, the message is nice, but it could be restricted to a specific assumed mechanism and supporting matrix.

Response:
We thank the reviewer for the constructive and inspiring comments. We fully agree that support also plays a key role in electrochemical reactions, as indicated in the literature The activity trends of 86 MM@Gr along the OCM for OER are shown as heat map in Figure R7, with all oxygenated intermediates as the most stable conformation (Tables R11-R14). Analogous to Notably, although the OER activity by OCM path on MM@Gr was inferior, the critical intermediates follow the same scaling relationship in Fig. 4b, albeit with a different support ( Figure   R9), indicating a general rule of OCM on DACs.      Tables 57-60). In analogy to Fig. 2b, the heat map also clearly shows a progressively improved activity from left to right, indicating that early-transition metal doping disadvantages the OER performance in either N-doped or defective graphene. In contrast to Fig. 2b, the quantities of DACs with high activity on defective graphene support are much less than that on N-doped graphene support, following the order FeFe(0.38V) = CuPd(0.38V) Based on the analysis of the free energy diagrams ( Supplementary Fig. 9 14, 3766-3772 (2014).

Supplementary Figure and Table:
Figure R6 has been included in Supplementary Fig. 7. Figure R7 has been included in Supplementary Fig. 8. Figure R8 has been included in Supplementary Fig. 9. Figure R9 has been included in Supplementary Fig. 12.

Comment 2:
The overpotential calculation does not account for the barrier for O2 desorption, I guess because it is not an electrochemical process. However, if O2* is largely stable, the barrier for its desorption could be higher than the eta. Did the authors considered this? Figure S5 shows many cases where O2* is strongly stable.

Response:
We are thankful to the reviewer for the professional comment. Given that the desorption of gaseous CoM, NiM and CuM using the desorption free energy of NiFe-CNG as a benchmark (ΔG*O2O2(g) = 1.17 eV), and found that the ΔG*O2O2(g) of all 8 highly active DACs screened was below 1.17 eV (Table R15). Figure S5 can be calculated by

Revisions:
Page 12, Line 11: "It is worth noting that *O2O2(g), as a non-electrochemical process, 79 is not appropriate to be included in the elementary steps, which overestimates the overpotential and misjudges the PDS."  Comment 3: Figure 6 and the related discussion look obscure to me. They state that: " Fig. 6a shows that the screened highly active DACs prefer second OH adsorption (except for CoCu) over competitive OH deprotonation, suggesting that these DACs are selective for OCM rather than AEM" If I read correctly the figure in several cases, about half, O* formation is more favorable than OH*OH* one. This point is related to point 1.2.
Also, they suggest some correlation between M1-M2 distance and the overpotential, figure 6b, but if I read correctly the figure, the data are broadly scattered.

Response:
We thank the reviewer for the comment. What we want to express is that the 7 heteronuclear and

Revisions:
Page 19, Line 5: "We also plotted the M1-M2 distance versus η, as shown in Supplementary Fig. 22, with the appropriate range favoring the occurrence of OCM."

Comment 4:
The section devoted to Bader charge analysis, charge density plots etc should be moved to the SI. They make more diluted the main findings.

Response:
We thank the reviewer for the comments. We have moved Fig. 7 in the original manuscript to Figure S18 in the revised Supplementary information.

Response:
Thank you for this comment. We have modified Fig. 3 in the revised manuscript.

Response:
We thank the reviewer for the constructive comments. As mentioned in the literature (ACS Catal. 2022, 12, 11682-11691), peroxide or superoxide nature of *O2 complexes play an important role on SACs for OER, which could be the same on DACs. Therefore, we inspect the nature of *O2 complexes along OER path for the highly active DACs screened, which are shown in Fig. 3 in the revised manuscript and Supplementary Fig. 12.
Furthermore, as suggested by the reviewer, we found a correlation between the charge amount of *O2 received from the slab and the O-O bond length of *O2 ( Figure R10a), implying that the more charge *O2 receives, the longer the bond length. Particularly, after excluding the disturbance data of DACs with ΔG*O2O2(g) > 1.17 eV (see response for Comment 2), this linear correlation is more satisfactory ( Figure R10b). Therefore, the O-O distance of *O2 can be employed as a useful descriptor to describe the charge transfer. In addition, to better understand the possible relationship between the bond length and the O2 desorption, we also plotted the correlation with bond length and ΔG*O2O2(g).
Unfortunately, no strong correlation exists between the both, which is possibly caused by the wide energy range of theΔG*O2O2(g) (Figure R10c, d). Relationship between *O2 bond length and ΔG*O2O2(g).

Revisions:
Page 12, Line 13: "Inspired by the literature, 56 *O2 exhibits peroxide or superoxide characteristics in two different adsorption modes, end-on and side-on, respectively, due to the different combinations that induce variation in O-affinity. Supplementary Fig. 2 illustrates the specific adsorption configurations which are indicated in Fig. 3 as the peroxo-or superoxide nature of *O2."

Page 12, Line 22:
"To better understand the significance of *O2, a correlation between the charge amount of *O2 received from the slab and the O-O bond length of *O2 (Supplementary Fig. 6a) can be established, implying that the more charge *O2 receives, the longer the bond length. Particularly, after excluding the disturbance data of DACs with ΔG*O2O2(g) > 1.17 eV, this linear correlation is more satisfactory (Supplementary Fig. 6b). Therefore, the O-O distance of *O2 can be employed as a useful descriptor to describe the charge transfer. In addition, we also plotted the correlation with bond length and ΔG*O2O2(g). Unfortunately, no strong correlation exists between the both, which is possibly caused by the wide energy range of the ΔG*O2O2(g) (Supplementary Fig. 6c, d)." Page 10, Line 10: Fig.3 has been revised below.

Reviewer #2 (Remarks to the Author):
In this manuscript, a large-scale DFT was employed to explore the feasibility of *O-*O coupling mechanism, which can circumvent the scaling relationship on improving the OER performance of DACs. In addition, the chemical and structural origin in favor of *O-*O coupling mechanism thus leading to enhanced OER activities have been revealed. However, the analyses of Gibbs free energy and overpotential are probably wrong, the conclusions lack innovative. The reviewer suggests that if the author thoroughly revises this manuscript, it may be reconsidered for publication in this journal.

Response:
Many thanks for the reviewer's comments, which provide us another chance to further improve the quality of our paper. We have carefully modified the manuscript and Supplementary Information according to your constructive comments. Additionally, we demonstrate that the two O atoms are directly coupled after *OH-*O deprotonation, rather than as two isolated *O atoms. Energetically, the configuration of *O2 formed by *O-*O coupling is lower and more stable than the configuration before coupling (Table R16)

Revisions:
Page 17, Line 4: "Additionally, the kinetic process of *O-*O coupling is also critical for triggering OCM, and higher kinetic barriers reduce the potential for OCM to occur. Therefore, we further calculated the possible coupling processes based on the 8 heteronuclear DACs screened ( Supplementary Fig. 17 and Table 80  the first *OH is adsorbed in the middle of the dual-atom, then the adsorption behavior of the second *OH has a stereo-hindrance effect. Therefore, the different adsorption behavior of the second *OH should be discussed, e.g. on the other side of the catalyst, on the adjacent C atom, etc.

Response:
Thanks for the constructive comments from the reviewer. Regarding the reviewer's concern, we performed additional calculations to investigate the selectivity of the different adsorption behavior of and Tables R17-R20), which circumvents the effect of the adjacent C site for *OH adsorption. Likewise, we also investigated the possibility of the second *OH adsorption on the other side of the DACs, which can be achieved for nearly half of the 86 DACs ( Figure R14b and Table R17)

Revisions:
Page 11, Line 27: "The above analysis on activity is based on the hypothesis that both *OH are adsorbed on the metal dimer, and whether alternative adsorption behavior is possible? For example, the second *OH adsorbs on the adjacent C site, or on the reverse side of the catalyst. 48,55 As shown in Supplementary Fig. 5a and Supplementary Tables 52-55, virtually the   property, and secondly, the energy barrier of the step *O-*O→O2 is generally higher, therefore, the author needs to calculate the transition state, or even the kinetic pathways of the OCM.

Response:
We thank the reviewer for the comment. Actually, the reason we proposed OCM in the manuscript is that the two adjacent active sites of DACs could provide the feasibility of *O-*O coupling. More specifically, the occurrence of OCM, not AEM, lies in the feasible adsorption of second *OH on the metal dimer, which avoided the generation of *OOH, rather than depends on the adsorption configuration of *O2. Regarding the reviewer's concern that many selected DACs are *OO structures more stable than *O-*O, the combination of O2 with DACs can be classified into two configurations, the end-on configuration with superoxide character and the side-on configuration with peroxide character (J. Catal. 2023, 417, 351-359), with all *O2 configurations necessarily to be thermodynamically most stable, which excludes artificiality in the selection of configuration. The adsorption of O2 in the present study involves both of the above conformations, as updated in Fig. 3 in the revised manuscript.

Revisions:
Page 10, Line 1: Fig.3 has been revised below. Page 17, Line 4: "Additionally, the kinetic process of *O-*O coupling is also critical for triggering OCM, and higher kinetic barriers reduce the potential for OCM to occur. Therefore, we further calculated the possible coupling processes based on the 8 heteronuclear DACs screened ( Supplementary Fig. 17 and Table 80

Supplementary Figure and Table:
Figure R15 has been included in Supplementary Fig. 17.

Comment 4:
The mechanism, OCM, that the author summarized, applies to both acidic and alkaline electrolytes. However, like the AEM, the potential-determining step is generally different for acidic and alkaline electrolytes, and the author needs to add discussions based on the calculation results.

Response:
We thank the reviewer for the comment.  Funct. Mater. 2022, 32, 2207110). Although its η increases with the values of pH, the η is still lower than 0.44 V at pH = 13 ( Figure R19), which is similar to the results calculated with the CCM. In addition, it is demonstrated that the potentialdetermining step does not change under different pH conditions. Therefore, CCM, which is commonly adopted in the theoretical OER studies, still has the ability to quantitatively characterize reactivity (Nat. Commun. 2023, 14, 112), and CPM is our research interest in the future.
[Redacted] Comment 5: It is necessary to carefully verify the rightness of the data for the OCM of NiPd@NC, because, the data do not theoretically match the given structures and mechanism. If the data are verified to be right, the author needs to analyze the electronic properties such as Bader charge for each step of the OCM of NiPd@NC. 98

Response:
We thank the reviewer for carefully reviewed the manuscript and pointed out our oversight. We apologize for the confusion between NiPd and NiPt. We have corrected this error in the revised version and listed the electronic structure information for NiPd, NiPt, CuPd and CuPt in Supplementary   Information (Figures R20 and R21).   Table: Figure R20 has been included in Supplementary Fig.18. Figure R21 has been included in Supplementary Fig.21.

Reviewer #1 (Remarks to the Author):
The authors have clarified some aspects raised by the referee and better discussed the novelty of their work. They have also performed several additional calculations to corroborate their findings. Therefore, the effort is largely appreciated. However, I must say that there are parts that are still unclear and somewhat contradictory, and given the highlevel nature of the journal I still can not provide a positive recommendation. If the authors could address the following points the article could be suitable for Nat. Comm..
Based on the authors claims, they are proposing that i) the O-O coupling mechanism is preferred on Dual Atom Catalsts, ii) the formation of OH*OH* leads to scaling relationships different from those of the standard O* and OOH* OER intermediates, iii) a solid recipe for the catalyst optimization is proposed. As I mentioned in the previous round, it was already reported that the O-O coupling mechanism is preferred [10.1016/j.jcat.2022.12.014] (on Single Atom Catalysts) and that OH*OH* brakes the scaling relatioships [10.1021/acscatal.0c00815]. In this respect, the work provides a further step in this direction but the fact that previous works have already shown similar result is somewhat not sufficiently clear in the revised version of the work.
An important aspect to underline is that the nature of journal implies a clear-cut novelty and insight, and one could expect to find a clear recipe for the catalyst optimization, also because of the previous discussion. Instead, based on very large number of calculations one can extract some candidates but no descriptors (see point below) for future predictions are present. Figure 6a shows that many cases have O* more stable than OH*OH*, and this partly contradicts the first (i) conclusion, and most importantly it does not allows to use the free energy of OH*OH* as a descriptor. A clear explanation for this discrepancy is needed.

Reviewer #2 (Remarks to the Author):
The author answered all questions correctly and I suggest that this paper can be accepted.

Manuscript ID: NCOMMS-22-48108A
Title: Synergy of Dual-atom Catalysts Deviated from the Scaling Relationship for the Oxygen

Evolution Reaction
At the outset, we would like to thank the Editor for providing us with one more opportunity to revise the manuscript. We are also very grateful to the reviewers for their time as well as valuable comments

Responses to the comments of reviewers:
Reviewer #1 (Remarks to the Author): The authors have clarified some aspects raised by the referee and better discussed the novelty of their work. They have also performed several additional calculations to corroborate their findings. Therefore, the effort is largely appreciated. However, I must say that there are parts that are still unclear and somewhat contradictory, and given the high-level nature of the journal I still can not provide a positive recommendation. If the authors could address the following points the article could be suitable for Nat. Comm.

Response:
We are glad that the reviewer finds improvements in the revised manuscript, many of which are spurred from the useful comments and suggestions from the reviewer. We would also like to thank the reviewer for the review and comments on our manuscript again. All remaining concerns have been taken into careful consideration in this revision, and a point-to-point response to the specific comments could be found in the coming paragraphs below. In order to further carry forward the above highly valuable investigations, unconventional mechanisms

Response:
Many thanks to the reviewer for giving us the opportunity to clarify the strengths of our research.
To the best of our knowledge, a large-scale investigation on dual-metal active sites for OER, particularly for the unconventional OCM mechanism, remains elusive. Therefore, our work contains four key findings: 1) Based on the large-scale screening of 86 DACs, a full picture of OER along the OCM is illustrated by means of an activity map, which facilitates the establishment of chemical intuitions to circumvent potentially poorly active DACs. Specifically, it is demonstrated that, even with different support, such as defective graphene, DACs incorporating early transition metals may not be suitable for achieving high OER activity through the OCM mechanism.
2) As distinct from SACs, the deviation of the scaling relationship caused by synergistic effects makes DACs that follow the OCM (or hybrid mechanism) superior candidates.
3) A universal descriptor, ΔG*OH-*OH, was obtained by rational design, which qualitatively or even partially quantitatively evaluated the OER overpotential, and successfully predicted high performance of homonuclear DACs. Significantly, the ΔG*OH-*OH descriptor as proposed would allow future researchers to quickly identify the activities of OER reactions along OCM by straightforward calculation of ΔG*OH-*OH. The applicability of the descriptors to *Oselective DACs is also possible as will be described in detail in the following section.
4) The trigger condition for OCM is a thermodynamic preference for the adsorption of a second *OH rather than the adsorption of *O. In addition, the activity as well as the regularity of DACs with sufficient amounts along the hybrid mechanism have been studied systematically for the first time.
An activity descriptor of ΔG*OH-ΔG*O for OER process via AEM mechanism has been previously reported, which in essence expects a constant rise of 1.23 eV for each elementary step resulting in an ideal η = 0. Similarly, the ΔG*OH-*OH descriptor is rationally designed for OCM mechanism based on the screening of high-performance DACs as a reference. The optimal range of ΔG*OH-*OH from 1.56 to 2.46 eV is also pertinent to a constant rise of 1.23 eV for each elementary step along the OCM and thus evaluating OER activity (as mentioned above). In addition, the applicability of the ΔG*OH-*OH descriptor for the hybrid mechanism will be discussed in the next section.
Furthermore, in order to make our research more instructive for the actual OER process, as well as to further enhance the novelty and insight of our work, preliminary calculations with the constant potential method (CPM) have been carried out and complemented in this revised manuscript. under acidic conditions. Notwithstanding, the results suggest the three DACs are promising catalysts via OCM mechanism under both acidic and alkaline conditions ( Figure R1 a-f).
2) As the applied potential increases, the maximum free energy change (ΔGmax) of the PDS gradually decreases until the overpotential is obtained at ΔGmax = 0 ( Figure R2). The oxygenated intermediates exhibit different binding strengths at different active centers, which is the principal factor contributing to the distinct activities of the three DACs under the same pH conditions.
3) With the pH decreased from 13 to 1, the relative position of the lines representing each elementary step in Figure R1 a-f shifted, particularly for the most potential PDS of the *OH-*O  O2, which caused changes in the overpotential and even the PDS ( Figure R1 a and b).

Revisions:
Abstract, Page 2: "Meanwhile, the effect of pH and potential on OER activity was clarified by employing grand canonical DFT (GC-DFT)."

Page 19, Line 18:
"pH-Dependent and Potential-Dependent OER Activity The above results based on conventional constant charge methods (CCM) demonstrate that the synergistic effect between the dual-metal active sites in DACs can enhance OER activity. To better simulate the electrochemical interface and to examine the effect of pH as well as potential on the reaction activity, we took advantage of the JDFTx code of the grand canonical DFT (GC-DFT) for the constant potential method (CPM) calculations (more details in the Supplementary Information), 85 which have been proved useful in recent electrochemical studies. 86,87 As an example, with the screened high-performance NiPd@NC, CuPd@NC and CuPt@NC, we adjusted the absolute electrode potential to change the pH and electrochemical interface potential (referenced to RHE) as shown in Fig. 7 and Supplementary Tables 81-83. Interestingly, the activity order evaluated by the two methods of CCM (Fig. 3) and CPM was consistent for the three DACs under alkaline condition. In addition, the change in pH triggered a change in PDS, rendering the higher η for CuPd than CuPt under acidic conditions. The order of η for these three DACs is 0.08 V (NiPd) < 0.18 V (CuPt) < 0.20 V (CuPd) in acidic conditions, and 0.10 V (NiPd) < 0.18 V (CuPd) < 0.28 V (CuPt) in alkaline conditions, respectively, indicating they are all potentially promising catalysts via OCM under both acidic and alkaline conditions." Page 21, Line 1: "As shown in Figs. 7a-f, the free energy changes (ΔG) of the elementary steps decreases as the applied potential increases until the overpotential is determined with the maximum ΔG = 0 ( Supplementary Fig. 23), and this is analogous to a recent study of (phen2N2)FeCl monolayer. 88 Furthermore, the PDS of the three DACs is *OH-*O  *O2 (for NiPd@NC and CuPd@NC at pH

Supplementary Table:
Tables S81-83 are added below.  18. Trasatti, S., Structure of the metal/electrolyte solution interface: new data for theory.
Comment 3: Figure 6a shows that many cases have O* more stable than OH*OH*, and this partly contradicts the first (i) conclusion, and most importantly it does not allow to use the free energy of OH*OH* as a descriptor. A clear explanation for this discrepancy is needed.

Response:
Thank you very much for this comment. Firstly, as clarified in Response to Comment 1, the conclusion (i) is actually not mentioned in our manuscript. Instead, our high-throughput calculations indicated that only 11 out of 105 DACs are highly active via OCM with the possibility of breaking the 0.37V bottleneck.
Second, we want to clarify the point that the cases with *O more stable in Fig. 6a are less than half (*OH-*OH: *O = 56:49). Specifically, it would be arbitrary to completely discount the possibility of AEM on DACs, and we prefer to remind relevant researchers that OCM or even hybrid mechanisms cannot be ignored, as mentioned in the literature [10.1016/j.jcat.2022.12.014], and note that the 10 highly active DACs screened prefer OCM (except for CoCu).
The reviewer's concern about the potential unsuitability of employing ΔG*OH-*OH as a descriptor for characterizing the *O-selective DACs is legitimate. We will address this concern in two aspects: 1) The volcano plot of Fig. 5a in the manuscript applies in general to the OER process along the OCM (strictly speaking, not other mechanism). In the absence of knowledge of which mechanism, a certain DAC follows, the OCM can be preselected first. It is sufficient to obtain ΔG*OH-*OH (1.56 eV -2.46 eV) to judge the reactivity along the OCM. Following such an efficient screening, it is reasonable and necessary to evaluate the *O-selective DACs along the hybrid mechanism. With the narrowed scope of the screening, the second round of identifying *O-selective DACs is efficient and accurate. This can be reflected in the case of CoCu@NC, which is prejudged as potential active catalyst along OCM, and the secondary selection indicates the hybrid mechanism via *O-selective path is preferred (although without changing overpotential).
2) We further conclude that volcano plots employing ΔG*OH-*OH as the descriptor can still be exploited to qualitatively ascertain the overpotential of DACs, notwithstanding for *O-selective DACs ( Figure R3a). Specifically, the blue dots, as well as the volcano curve derived from Fig. 5a in the manuscript, are DACs with *O selectivity. To more accurately characterize the OER activity of these DACs with *O selectivity, we repositioned these DACs with ΔG*O as the descriptor (the purple dots). It was observed that DACs with ΔG*O as descriptor remained on the original volcano curve, which was attributed to the fact that the ΔG*OH/ΔG*OH-*OH scaling relationship virtually overlapped with that of ΔG*OH/ΔG*O ( Figure   R3b).
In summary, on the one hand ΔG*OH-*OH is generally applicable to OER processes along the OCM mechanism, and a secondary screening enables further rigorous identification of high-performance DACs with *O selectivity along hybrid mechanisms (e.g. CoCu). On the other hand, the fact that the